OSPF within what area is an OSPF router considered to be

In an OSPF topology, there can be many areas defined. Counterintuitively, OSPF routers do not belong to OSPF areas, but it is individual interfaces of OSPF routers that are assigned to areas.

Thus, it is inaccurate to state that particular routers belong to specific areas, unless all of their interfaces are within the area in question.

Routers with interfaces assigned to more than one area are considered Area Border Routers area border routers or ABRs. As is evident, it is not possible to state that an ABR belongs to any particular area, since it, by definition "belongs" to more than one.